# Triangle calculator

Please enter what you know about the triangle:
You have entered side a, c and angle α.

### Right scalene triangle.

Sides: a = 82   b = 66.48330805544   c = 48

Area: T = 1595.594393331
Perimeter: p = 196.4833080554
Semiperimeter: s = 98.24215402772

Angle ∠ A = α = 90° = 1.57107963268 rad
Angle ∠ B = β = 54.17111598996° = 54°10'16″ = 0.94554650999 rad
Angle ∠ C = γ = 35.82988401004° = 35°49'44″ = 0.62553312269 rad

Height: ha = 38.91769252026
Height: hb = 48
Height: hc = 66.48330805544

Median: ma = 41
Median: mb = 58.3876642308
Median: mc = 70.68223881883

Inradius: r = 16.24215402772
Circumradius: R = 41

Vertex coordinates: A[48; 0] B[0; 0] C[48; 66.48330805544]
Centroid: CG[32; 22.16110268515]
Coordinates of the circumscribed circle: U[24; 33.24215402772]
Coordinates of the inscribed circle: I[31.75884597228; 16.24215402772]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 90° = 1.57107963268 rad
∠ B' = β' = 125.82988401° = 125°49'44″ = 0.94554650999 rad
∠ C' = γ' = 144.17111599° = 144°10'16″ = 0.62553312269 rad

# How did we calculate this triangle?

### 1. Input data entered: side a, c and angle α. ### 2. From angle α, side c and side a we calculate side b - by using the law of cosines and quadratic equation:  Now we know the lengths of all three sides of the triangle and the triangle is uniquely determined. Next we calculate another its characteristics - same procedure as calculation of the triangle from the known three sides SSS. ### 3. The triangle circumference is the sum of the lengths of its three sides ### 4. Semiperimeter of the triangle ### 5. The triangle area using Heron's formula ### 6. Calculate the heights of the triangle from its area. ### 7. Calculation of the inner angles of the triangle using a Law of Cosines    